The Premier, Barry O'Farrell, said yesterday that Liberal MPs would get a conscience vote if the Greens presented a private member's bill next year to legalise medically assisted death.

Labor MPs will also have a conscience vote. The Nationals were undecided yesterday.

Opinion polls show Australians overwhelmingly support euthanasia but MPs have consistently rejected legislation to allow it.

Most of the MPs the Sydney Morning Herald spoke to yesterday opposed it, but favoured improvements in palliative care. ''I do have a strong religious belief but that's not really the perspective I come at it from,'' said the Liberal MP for Pittwater, Rob Stokes.

''Giving a person the legislative right to end the life of another person is incredibly difficult and fraught with danger.''

The Liberal MP for Hornsby, Matt Kean, agreed: ''My job as an MP, as a community leader, is to ensure that those most vulnerable in our community's rights are protected.''

In 2009 Mr O'Farrell said he strongly opposed euthanasia, and the Health Minister, Jillian Skinner, has repeatedly declared her opposition.

In 2002 the upper house voted down a Greens bill. The former Labor minister Carmel Tebbutt supported it and said she would probably vote that way again. ''I think it's right that people have an opportunity to be certain that their own views are going to be respected legally and that they can die with dignity,'' she said.

Scot MacDonald, a Liberal MLC, said his mind ''was not closed to it'' but he leant towards opposing it. ''I remember one of [my grandmothers] saying she wanted it to end … with tears running down her face she wanted to end it. It was undignified and painful,'' he said.

The Greens MP Cate Faehrmann, who will introduce the bill, said palliative care was sometimes not enough.

''There will always be a small percentage of people who do not have their pain and suffering alleviated by palliative care.''